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Virtual Resource Management in Green Cellular Networks with Shared Full-Duplex Relaying and Wireless Virtualization: A Game-Based Approach Gang Liu, Member, IEEE, F. Richard Yu, Senior Member, IEEE, Hong Ji, Senior Member, IEEE, and Victor C.M. Leung, Fellow, IEEE

Abstract—Recent advances in loop interference cancellation techniques enable full-duplex relaying (FDR) systems, which transmit and receive simultaneously in the same band with high spectrum efficiency. Meanwhile, wireless virtualization has attracted a lot of attentions from both academia and industry, because it can provide more flexibility, diversity, and other benefits in the process of wireless network design, construction, operation and management. In this paper, we introduce the idea of wireless virtualization into FDR cellular networks. Then, the problem of energy-aware virtual resource management is formulated as a three-stage Stackelberg game. The subgame perfect equilibrium for each stage is analyzed. In addition, the interplays of the threestage game are discussed and an iterative algorithm is proposed to obtain the Stackelberg equilibrium solution. Simulation results are presented to show the effectiveness of the proposed scheme. Index Terms—Full-duplex relaying; wireless virtualization; energy efficiency; resource allocation; Stackelberg game.

I. I NTRODUCTION

AND

M OTIVATIONS

Full-duplex relaying (FDR) systems are able to improve the spectrum efficiency significantly by transmitting and receiving simultaneously in the same band [1]. Although FDR was considered impractical in the past due to inherent loop interference, recent studies have shown the feasibility of FDR with the help of advanced interference cancellation techniques Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. This paper has been presented in part at the 2014 IEEE International Conference on Communications, Sydney, Australia. This work is jointly supported by the National Natural Science Foundation for Young Scholar (Grant No. 61302080), the National 863 project (Grant No. 2014AA01A701), and the National Natural Science Foundation of China (Grant No. 61571373). G. Liu is with Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, P.R. China. He is also with Key Lab of Information Coding and Transmission, Southwest Jiaotong University, Chengdu, 610031, China (email: [email protected]). F. R. Yu is with the Dept. of Systems and Computer Eng., Carleton University, Ottawa, ON, Canada. He is also with the College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, China (e-mail: [email protected]). H. Ji is with the Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, P.R. China (e-mail: [email protected]). Victor C. M. Leung is with the Department of Electrical and Computer Engineering, the University of British Columbia, Vancouver, BC V6T 1Z4 Canada (e-mail: [email protected]).

and transmit/receive antenna isolation [2]. Hence, FDR has re-gained the attention from both industry [3] and academia [4]–[7]. To tackle the loop interference problem in FDR systems, a broad range of mitigation schemes have been proposed, such as natural isolation, time-domain cancellation and spatial suppression [2], [8]. It has been shown that loop interference can be mitigated sufficiently, and FDR can be a feasible alternative to traditional half-duplex relaying (HDR) in future cellular networks. To evaluate the performance of FDR systems, the end-to-end SINR and capacity [9], outage probability [4] and diversity-multiplexing tradeoff [5] are analyzed. In addition, as observed in [10]–[12], residual loop interference may have significant impact on the performance of FDR systems due to the limited dynamic-range of transceiver and channel estimation error. In [12], the authors compare the end-to-end capacity of FDR and HDR systems while taking the residual loop interference into account. More interestingly, the authors in [10], [11] explicitly model the transceiver dynamic-range limitations and channel estimation error. And then, they also investigate the achievable rates of full-duplex MIMO relaying and full-duplex bi-directional communication systems. Moreover, an optimal power allocation scheme is proposed in [6] to minimize the outage probability for FDR systems. The authors of [7] investigate the joint optimization problem of resource allocation and scheduling to maximize the weighted throughput in full-duplex multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) relaying systems. Although some excellent works have been done for FDR systems, wireless virtualization in FDR networks is largely ignored in the existing literature. However, wireless virtualization has been considered as a promising technology for next generation wireless networks [13], and it is closely related to recent advances in software defined networking (SDN) [14]–[17]. Wireless virtualization can provide more flexibility, diversity, and other benefits in the process of wireless network design, construction, operation and management. Using wireless virtualization, physical wireless network infrastructure and physical radio resources can be abstracted and sliced into virtual wireless resources, and shared by multiple parties with a certain degree of isolation and customization [13].

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Although both FDR and wireless virtualization are promising technologies for next generation wireless networks, they have been separately studied in existing works. They are, in fact, closely correlated in next generation wireless networks. For example, on one hand, the full-duplex capability of FDR can be leveraged to facilitate the virtual resource slicing process in wireless virtualization; on the other hand, wireless virtualization can provide powerful and flexible resource management mechanisms for FDR networks to improve the performance. Moreover, energy efficiency is becoming an important design criterion in wireless systems because of the rapidly rising energy costs and increasingly rigid environmental standards [18]. Comparing with conventional HDR systems, the energy efficiency in FDR systems might be more crucial due to the presence of loop interference mitigation, which may cause inefficient use of the transmission power [19]. Also, resource management plays a very important role in energy efficiency, spectrum efficiency and quality of service (QoS) provisioning in traditional networks [20], [21]. Unfortunately, the existing resource management algorithms may not be directly applied in FDR systems because of the different manner of resource usage and the presence of loop interference in FDR systems. In addition, traditional resource management policies for FDR networks [7] and virtualized networks [22] generally optimize a unified objective in a centralized manner. They can not well describe the interactions between different entities (e.g., infrastructure providers and service providers) involved in resource allocation. The above observations motivate us to investigate the issue of virtual resource management in green cellular networks with FDR and wireless virtualization using a game-based approach. The distinct features of this paper are summarized as follows: •

•

Different from our previous work [19], we introduce the idea of wireless virtualization into FDR cellular networks. With wireless virtualization, the virtualized FDR networks can be decomposed into the following four logical roles: spectrum provider, base station provider, full-duplex relay station provider, and service provider. This decomposition enables flexibility, diversity, and other benefits in the process of cellular network design, construction, operation, and management [13]. With wireless virtualization, base station providers are able to share the same FDR. In this way, shared FDR deployment can improve the overall network performance by maintaining connections to multiple base stations and serving multiple users at the same time [23], [24]. Nevertheless, the considered system becomes a multipointto-multipoint FDR system, where the multi-access interference, multi-user interference and loop interference coexist at the same time. To the best of our knowledge, how to deal with these interferences together has not been well studied before. In this work, we propose a simple

•

and practical transmission policy to tackle the involved interferences. To well describe the interactions between different parties in resource allocation, the problem of virtual resource management is modeled as a three-stage Stackelberg game. In addition, energy efficiency is taken into account in the problem formulation. A widely used metric bits/Joule [20] is adopted to measure the performance of energy efficiency. Then, we analyze the subgame perfect equilibrium for each stage using a backward induction method. Also, we discuss the interplays between different stages and develop an iterative algorithm to obtain the Stackelberg equilibrium. The existence and uniqueness of the equilibrium solution are also discussed. Finally, extensive simulation results show that we can benefit from FDR and wireless virtualization simultaneously with the proposed scheme.

The rest of this paper is organized as follows. In Section II and III, the system model and problem formulation are presented, respectively. The proposed game is analyzed in Section IV. Simulation results are presented in Section V. Finally, we conclude this study in Section VI with future work. II. S YSTEM D ESCRIPTION In this section, we first describe the network model. Then, the transmission strategies for one-hop users and two-hop users are presented. A. Network Model As shown in Fig. 1, we consider a virtualized cellular network with shared full-duplex relaying. We consider the following four logical roles in cellular networks with FDR and wireless virtualization: spectrum provider, base station (BS) provider, full-duplex relay station provider, and service provider (SP). There are K spectrum providers, each of which owns one frequency band with variable bandwidth 1 and tries to sell it to BS providers to gain its profit. There are M BS providers. Each BS provider purchases appropriate amount of spectrum bands from spectrum providers and operates one BS per cell. Since virtualization is used, we adopt a cloud radio access network (C-RAN) based BS virtual resource manager (BS-VRM) [25] to abstract and manage the radio resources (e.g., BS, transmission power and spectrum band) of all the BS providers. Similar to [24], [25], each BS is connected to the BS-VRM via a high-capacity low-delay wired backbone, e.g., fiber. There is one RS provider, which owns one fullduplex relaying station [7] per cell2 . Decode and forward full-duplex relaying scheme is adopted at the RS. Similar to 1 Similar to that in cognitive networks [20], the bandwidth provided by spectrum provider is variable according to the demand and price of spectrum. 2 If there are multiple RSs in each cell, relay selection schemes [26] need to be adopted.



E E E

E.

each user of the SPs can access to the services via different access points (i.e., BS and RS) from different infrastructure providers (i.e., BS and RS providers). The SPs don’t need to know the channel state information (CSI) of their subscribers. What they need is to accept user’s access requests, schedule users, and report the results to BS-VRM and RS-VRM. Then, the BS-VRM and RS-VRM coordinate the process of resource management in the whole virtualized network. To facilitate the resource management process, we divide the two-hop users with similar channel condition and rate requirement into several groups employing user paring algorithm in [28], and each group has at most M users. Hence, the two-hop users in the same group can share the same band. Assume that K1 one-hop users and K2 groups of two-hop users are scheduled and served by all the SPs in a certain time slot. Quasi-static flat-fading is considered and OFDMA multiple access scheme is used. Similar to [23], we adopt a simple intra-sector routing metric where users are partitioned to onehop users and two-hop users based on their received signal strength from the base stations and the relay. The transmission policies for one-hop and two-hop users are introduced in the following. It is worth noting that the energy efficiency has been taken into account in the transmission policies. B. Transmission Strategies for One-hop Users

Fig. 1. The architecture of virtualized cellular networks with shared fullduplex relaying.

[7], error-free decoding3 is assumed at the RS. Moreover, the RS is virtualized and shared by all the BS providers via base station coordination and zero-forcing beamforming technologies [24], [27] described in the following parts. The RS provider borrows the resources (e.g., BS and spectrum band) from BS providers to provide wireless access service for two-hop users. The radio resources (e.g., transmission power and borrowed spectrum bands from BS providers) of the RS is virtualized and managed by a RS-VRM. Since the RS is able to transmit and receive data simultaneously in the same band, it leads to different manner of resource allocation from traditional half-duplex relaying stations. Service providers try to provide different services to their subscribers via the same substrate network. One-hop users are directly served by the nearest BS and two-hop users connect to BSs indirectly with the help of the RS. Each user and BS is equipped with one antenna. The shared RS is equipped with M antennas. Hence, the RS is able to connect to M BS simultaneously and can serve at most M two-hop users at the same time in the same band through spatial division. With the proposed architecture, all the SPs can share the same substrate network which consists of BSs and RS. Hence, 3 This assumption is reasonable since the data rate of scheduled user is always less than the instantaneous channel capacity. Thus, an arbitrarily small error probability can be achieved with a powerful error correcting code [7].

For one-hop user i (i = 1, 2, ..., K1), let gij be the channel gain in band j of user i from its nearest BS, and pij is the power assigned to user i in band j. Since OFDMA multiple access scheme is used, a band can only be allocated to a onehop user or a group of two-hop users. If band j is assigned to user i, then the band allocation indicator aij = 1; Otherwise, aij = 0. Then, the energy efficiency of one-hop user i can be expressed as follows PK gij pij j=1 aij bj log2 (1 + δ 2 ) bits/Joule (1) ηi = PK pb + j=1 pij where pb denotes the circuit power at the corresponding base station which includes the energy consumption of mixers, filter, and digital-to-analog converters. Moreover, pb is independent of the data transmission power. Without loss of generality, we assume the noise variance δ 2 is the same for all the users and RSs. Note that the energy efficiency metric bits/Joule in (1) is a widely adopted in the existing literature on energy-efficient communications [18], [29]. C. Transmission Strategies for Two-hop Users Since the RS is shared by all the BSs, the downlink transmission of two-hop users in a same group works as follows. On one hand, the BSs transmit user data to the shared RS coordinately. One the other hand, the RS forwards the received data to designated two-hop users. Since fullduplex relaying scheme is adopted, these two actions happen at the same time on the same frequency band. Therefore, the



downlink transmission of the two-hop users in the same group can be split into two parts: feeder link (from the BSs to the RS) and access link (from the RS to two-hop users). The direct links between BSs and two-hop users are ignored due to large path-loss, shadow effects and obstacles. The signal model for feeder link is actually a multi-access channel. The received signal at the RS involves both loop interference and multi-access interference. In order to mitigate the loop interference, a time-domain loop interference cancellation technology in [2] is employed at the relay receiver. More specifically, an estimated copy of the self-interference signal is subtracted from the received signal of the RS and this can be implemented in either analog or digital manner [8]. In order to eliminate the multi-access interference, we can apply the multi-user detection technologies. However, for the consideration of complexity, we adopt a MMSE receiver [7] to separate signals from different BSs, which can also further suppress the residual loop interference. To facilitate the transmission in feeder link, base station coordination [30] can be applied to make distributed BSs act as a single M -antenna transmitter. In this way, the feeder link could be regarded as a virtual point-to-point MIMO channel, and classical MIMO technologies [31] can be applied to parallelize the feeder link. With the base station coordination technology, the CRAN based BS-VRM is able to optimize the transmission beamforming matrix at the BS to combat the multi-access interferences. Therefore, the RS is virtualized and shared by different BSs without additional multi-access interferences. Assume two-hop users in group i are served in band j. Let Hij ∈ CM×M be the channel matrix from the virtual BS antenna array to the RS in band j, and its singular value M×M decomposition is Hij = Uij Σij VH is ij , where Σij ∈ C m a diagonal matrix consists of M singular values {σij } of Hij . According to [31], the virtual point-to-point MIMO channel from BSs to the RS can be decomposed as M independent parallel subchannels. Similar to (1), the energy efficiency of the feeder link for two-hop users in group i can be denoted as m m PM PK σij pij m=1 bj log2 (1 + j=1 aij δr2 ) (2) ζi = P PM m pb + K j=1 m=1 pij

where aij is the band allocation indicator and pm ij is the transmit power assigned to subchannel m. In addition, δr2 is the equivalent variance of the total of noise and residual loop interference. According to [2], [10], [11], the residual loop interference is mainly caused by the limited dynamic-range of the full-duplex relay transceiver and the estimation error of the loop interference channel. Similar to [12], δr2 is modeled as δr2 = δ 2 + δe2 , where δe2 is the variance of residual loop interference. In fact, the access link is a typical broadcast channel. To orthogonalize the data streams for different two-hop users in the same group, we adopt the well-known zero-forcing beamforming [27] in the access link. In this way, the multi-

Stage ĉ Spectrum Provider

Spectrum Band

FM

E

F

Stage Ċ BS Provider

F.

EM

^DLM Lę Stage ċ RS Provider

^DM` ¨

^D .M` ¨.

One-hop user 1 One-hop users

One-hop user K1

`

^§Lę L `

RS_VRM

D. M Service Provider

E.

C-RAN Based BS_VRM

.

D. . M . .

Group 1

Group K2

Two-hop users

Fig. 2. Three-stage Stackelberg game modeling({aij }: the set of band allocation indicator for the ith user; Φ2 : the set of index for two-hop users.)

user interference between two-hop users in a same group can be totally eliminated. Let Gij ∈ CM×M be the equivalent channel matrix from the RS to the two-hop users in group i in band j. Then, according to [27], the transmission rate of access link for two-hop users in groupmi mcan be expressed PM PK γ q m as Ria = j=1 aij m=1 bj log2 (1 + ijδ2 ij ), where γij = 1 m and q are the effective channel gain and −1 ] ij [(Gij GH m,m ij ) transmit power for two-hop user m in group i in band j. [A]m,m denotes the mth element in the main diagonal of matrix A. Similarly, the energy efficiency of the access link for two-hop users in group i is expressed as m m PM PK γij qij m=1 bj log2 (1 + δ 2 ) j=1 aij ςi = (3) P PM m pr + K j=1 m=1 qij where pr is the circuit power at the relay station and it is also independent of the data transmission power. III. E NERGY-AWARE V IRTUAL R ESOURCE M ANAGEMENT P ROBLEM F ORMULATION In the virtual resource management process, the spectrum providers first determine the price for each band to maximize their total profit according to the demand of the BS providers. Secondly, the BS-VRM purchases appropriate amount of spectrum bands from the spectrum providers and then allocate them to one-hop users and the shared relay. At last, the RSVRM decides the appropriate power level for two-hop users. Based on the observations above, the energy-aware bandwidth sharing and power allocation problem in the virtualized full-duplex relaying networks can be formulated as a threestage Stackelberg game model (as shown in Fig. 2). In our proposed game, the up-stage acts as leader, which makes decision first. The down-stage is the follower and moves subsequently on the basis of the leader’s strategy. In stage I, the spectrum providers serve as leader and offer the price cj for each band bj according to the band demand of the BSs. In stage II, the BS providers, as the follower of stage I, decide how many and which bands to purchase from the spectrum providers based on the price of each band. And then,



the BS-VRM, as the leader of stage II, sells the bands and power to one-hop users and the feeder link of two-hop users to gain their profit. In stage III, the RS-VRM, as the follower of stage II, performs resource allocation for the access link of two-hop users to gain its revenue. Since the decisions of leaders will affect the strategy of the followers, to formulate this three-stage Stackelberg game model, it is wise to adopt the backward induction method as follows. In stage III, the RS-VRM performs optimal power allocation to maximize its profit, which has taken the energy efficiency of each access link for the two-hop users into account. For two-hop users in group i, the energy efficiency of their access link is given in (3). Then, we define the utility of the RS on the access link for the two-hop users in group i as URS,i = αi ςi − βi ςi (4) where αi and βi can be interpreted as the revenue and cost to transmit one bit of data, respectively. Moreover, βi is charged by the BSs due to the assigned bands. Then, the utility function is the profit of the RS gained from the data transmission using one Joule of energy for the access link of two-hop users in group i. Note that we assume αi > βi . Otherwise, the RS will not provide service for two-hop users in group i. In stage II, the responsibility of BS-VRM is to purchase bands from the spectrum providers and allocate the bands and power to one-hop users and the feeder link of two-hop users. The aim of the BS-VRM is to maximize the total profit of BSs while considering the energy efficiency of one-hop users and the feeder link of two-hop users. Inspired by [32], we assume the band demand bj satisfies linear structure. Then, the utility of the BS-VRM is defined as a quadratic utility function [33] as follows UBSs =

K1 X i=1

εi ηi +

KX 1 +K2

(βi ςi + ρi ζi ) −

i=K1 +1

K X

cj b j

j=1

  K X 1 X 2 − b + 2ν bi bj  2 j=1 j

(5)

i6=j

where εi and ρi represent the revenue obtained from onehop user i and the feeder link of two-hop users in group i, respectively, cj is the price of band bj offered by the spectrum PK1 +K2 providers, i=K βi ςi is the cost paid by the RS to the BS1 +1 VRM, and ν ∈ (−1, 1) is the band substitutability parameter. ν = 1 implies that the one-hop users or two-hop users can switch among the bands freely; ν = 0 means that the one-hop users or two-hop users can not switch among the bands; ν < 0 means that the bands used by one-hop users or two-hop users are complementary. Note that the motivations to choose the quadratic utility function in (5) are mainly as follows: 1) It is concave with respect to the band demand bj , and this makes it easy to obtain the maximum revenue of the BSs. 2) The band demand

function can be readily obtained by differentiating the utility function (5). It will be found that the band demand is a linear function with respect to the price of the corresponding band. 3) It can also be found that the price of one band may affect the band demand of another band. Therefore, the fourth term in (5) is used to describe the relationship between different bands as described in [33]. In stage I, the goal of spectrum providers is to maximize their total profit by offering the price cj according to the band demand bj of the BSs. Hence, the total revenue of the spectrum providers can be denoted by the following utility function K X (cj bj − wj bj ) (6) UT = j=1

where wj is the cost of band bj for the spectrum providers. Usually, we have cj ≥ wj ; Otherwise, the spectrum providers will not sell the band bj to the BSs. IV. A NALYSIS OF THE P ROPOSED T HREE -S TAGE S TACKELBERG G AME In this part, the proposed game is analyzed in a backward induction manner. After each stage is solved in Subsections IV-A, IV-B and IV-C, the interplays between them and the Stackelberg equilibrium are discussed in Subsection IV-D. A. Stage III: Energy-Efficient Power Allocation for RS By observing (1), (2) and (3), we realize that the energy efficiency expressions of one-hop and two-hop users take the similar form. Therefore, in this subsection, we will only give the power allocation policy for the access link of two-hop users. As for one-hop users and the feeder links of twohop users, the power allocation policies can be obtained in a similar way. After investigating the property of the utility function of the RS, we have the following theorem. Theorem 1: For the access link of two-hop users in group i, the utility function URS,i in (4) is strictly quasiconcave with respect to the power allocation vector qi = 1 2 M 1 2 M T [qi1 , qi1 , ..., qi1 , ...qiK , qiK , ..., qiK ] . Furthermore, there exits a unique optimal power allocation vector q∗i , which satisfies h ′ i > 0, URS,i is 1) When Ria (pr + Pt (qi )) − Ria (0) |qi =qi

first strictly increasing h i and then strictly decreasing in ∂U m qij and hence ∂qRS,i = 0. m ij |qi =q∗ i i h ′ < 0, URS,i is 2) When Ria (pr + Pt (qi )) − Ria (0) |qi =qi

m strictly decreasing in qij and hence q∗i = 0. ′

∂Ra

where Ria is defined in Section II-C, Ria = ∂qmi , ij PK PM m and Pt (qi ) = j=1 m=1 qij (0) m−1 m+1 1 2 M 1 2 M T , qi1 , ..., qi1 , ..., qij , 0, qij , ...qiK , qiK , ..., qiK ] . qi = [qi1 Proof: Denote the upper contour sets of the utility function URS,i as Sα = {qi 0|URS,i ≥ α}, where qi 0 implies that each element of qi is nonnegative. According to



the Definition 3.4.1 of [34], URS,i is strictly quasi-concave if and only if Sα is strictly convex for any real number α. It is easy to verify that when α < 0, Sa is null set. When α = 0, only qi = 0 satisfies URS,i = α. Therefore, when α ≤ 0, Sa is strictly convex. P WhenP α > 0, Sa can be rewritten as K M m Sa = {qi 0|α(pr + j=1 m=1 qij ) − (αi − βi )Ria ≤ 0}. PK PM m Since α(pr + j=1 m=1 qij ) − (αi − βi )Ria is convex with respect to qi , so is Sa . Hence, URS,i is strictly quasi-concave. To prove the existence and uniqueness of the optimal power allocation vector qi , the first partial derivative of URS,i with m respect to qij is obtained as follows ′

(αi − βi )[Ria (pr + Pt (qi )) − Ria ] (pr + Pt (qi ))2 (αi − βi )Ψ(qi ) = (7) (pr + Pt (qi ))2 PK PM ′ ∂Ra m where Ria = ∂qmi and Pt (qi ) = j=1 m=1 qij . To ij investigate the monotonicity of URS,i , we need to know whether Ψ(qi ) is bigger than zero or not. Hence, we compute ′′ ′′ Ψ′ (qi ) = Ria (pr + Pt (qi )), where Ria is the second ′′ m derivative of Ria with respect to qij . Since Ria < 0, then Ψ′ (qi ) < 0. Therefore, Ψ(qi ) is strictly decreasing. Moreover, we have  aij bj (pr + Pt (qi )) lim Ψ(qi ) = mlim  2 m −>∞ m) qij qij −>∞ ln 2( γδm + qij ij  M K m m X X γij qij aij bj log2 (1 + − ) δ2 m=1 j=1 ∂URS,i m ∂qij

According m −>∞ limqij

=

to

aij bj (pr +Pt (qi )) 2 ln 2( γδm ij

lim m

qij −>∞

K X j=1

m) +qij

aij

L’Hopital’s rule aij bj = ln . In addition, 2

M X

bj log2 (1 +

m=1

[35],

m m γij qij )=∞ 2 δ

m −>∞ Ψ(q ) = −∞. Therefore, limqij i m −>0 Ψ(q ) In addition, limqij i i h ′ a a , where Ri (pr + Pt (qi )) − Ri (0)

[n+1]

2: 3:

4: 5: 6:

kq

= (0) qi

=

is first positive and then becomes negative with the increase of m qij . Hence, URS,i is first strictly increasing and then strictly m . In addition, the optimal power allocation decreasing in qhij i ∂U

= 0. policy satisfies ∂qRS,i m ij |qi =q∗ ii h ′ < 0, then If Ria (pr + Pt (qi )) − Ria (0)

∂URS,i m ∂qij m qij and q∗i =

ǫ do kqi k1 Search for optimal step size µ using gradient assisted binary search i+ h in [29] [n] [n] [n+1] = qi + µ∇URS,i (qi ) qi end for Output the optimal power allocation vector q∗i .

obtained by solving nonlinear equation. However, this suffers from high computational complexity. Fortunately, since the utility function (4) is strictly quasi-concave, the following binary search assisted ascent algorithm can be adopted to realize the energy-efficient power allocation for the access [n] links. In Algorithm 1, ∇URS,i (qi ) is the gradient of URS,i at iteration n and the global convergence is guaranteed by the strict quasi-concavity of URS,i [29]. It is also discussed in [29] that the computational complexity can be reduced significantly with the help of binary search assisted ascent algorithm. B. Stage II: Optimal Bandwidth Sharing for Users After the energy-efficient power allocation policy of RS is determined, the BS-VRM will decide the optimal size of bands to purchase from the spectrum providers and allocate the bands to different users in this part. Since the utility function of BS-VRM in (5) is concave with respect to the band demand bj , the optimal band demand b∗j , which maximizes the utility, can be obtained by solving dUdbBSs = 0, i.e., j K1 X

aij εi ηij +

KX 1 +K2

aij (βi ςij +ρi ζij )−cj −bj −ν

i=K1 +1

i=1

|qi =qi m−1 m+1 1 2 M 1 M T [qi1 , qi1 , ..., qi1 , ..., qij , 0, qij , ...qiK , q 2 , ..., qiK ] . i iK h ′ ∂U a a > 0, ∂qRS,i Therefore, if Ri (pr + Pt (qi )) − Ri m (0) ij |qi =qi

|qi =qi

Algorithm 1 Energy-efficient power allocation based on binary search assisted ascent algorithm 1: Initialization [0] Initialize the default transmission power vector qi and i+ h [0] [0] [1] step size µ. Set qi = qi + µ∇URS,i (qi ) . (Search for optimal q∗i )

ζij =

PM

pb +

p

log2 (1+ ijδ2 ij ) P , pb + K j=1 pij m pm σij ij

log2 (1+ PK PM

m=1

j=1

bi = 0

i6=j

g

where ηij =

X

2 δr

m m=1 pij dUBSs

)

ςij =

PM

pr +

m qm γij ij ) δ2 m q m=1 ij

log2 (1+ PK PM

m=1

j=1

and

. For each j = 1, 2, ...K, we have a

similar equation dbj = 0. After after adding them together and several manipulations, the optimal band demand b∗j is given as follows PK ν(Kκ − i=1 ci ) κ − cj − (8) b∗j = 1−ν (1 − ν)[1 + ν(K − 1)] P 1 PK1 +K2 where κ = K i=1 aij εi ηij + i=K1 +1 aij (βi ςij + ρi ζij ). Actually, b∗j is the best reaction function [36] for the bandwidth price cj . As we assumed in (5), it is a linear function with respect to cj . In addition, we can also notice that b∗j is a function of the band allocation indicators aij and the power



allocation policy in Subsection IV-A. Different band allocation policy leads to different band demand b∗j and different revenue UBSs of the BS-VRM. Therefore, how to allocate the bands to different users is an important problem. For the purpose of maximizing the profit of BS-VRM, we develop an alternating direction method of multipliers (ADMM) [37], [38] based spectrum band sharing algorithm as follows.

the following problem with an initial spectrum band demand:  KX K1 K 1 +K2 X X cj b j εi ηi + (βi ςi + ρi ζi ) − max {aij }  j=1 i=1 i=K1 +1   K  X 1 X 2 (9) − bj + 2ν bi bj   2 j=1

1) Introduction to Alternating Direction Method of Multipliers: ADMM [37], [38] is a simple but powerful algorithm that is well suited to distributed convex optimization. One of the important properties of ADMM is its quick convergence to a modest accuracy of the optimal solution, which is desirable for engineering problems like the considered virtual resource management problem. It has been successfully used in statistical learning problems, engineering design, multi-period portfolio optimization, network flow, scheduling and so on [37]–[40]. It takes the form of a decomposition-coordination procedure, in which the solutions to small local subproblems are coordinated to find a solution to a large global problem. Furthermore, ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization [37], [38]. Generally, ADMM is able to solve min f (x) + g(z), x,z

s.t. Ax + Bz = c, where x ∈ Rq×1 , z ∈ Rr×1 , A ∈ Rp×q , B ∈ Rp×r and c ∈ Rp×1 . There are two basic forms for ADMM algorithm, namely unscaled form and scaled form. In the unscaled form, the augmented Lagrangian is given as Lρ (x, y, z) = f (x) + g(z) + yT (Ax + Bz − c) + (ρ/2) k Ax + Bz − c k22 , where y ∈ Rp×1 is the dual variable vector, ρ > 0 is a predefined augmented Lagrangian parameter and k · k2 is an Euclidean norm operator. Accordingly, the unscaled ADMM consists of the following iterations: xt+1 := arg min Lρ (x, yt , zt ), zt+1 := arg min Lρ (xt+1 , yt , z) and x

z

yt+1 := yt + ρ(Axt+1 + Bzt+1 − c), where t is iteration index. In the scaled form, the augmented Lagrangian is rewritten as Lρ (x, y, z) = f (x) + g(z) − (ρ/2) k µ k22 +(ρ/2) k Ax + Bz − c + µ k22 , where µ = (1/ρ)y is the scaled dual variable vector. In this case, the iterations of ADMM can be expressed as: xt+1 := arg min(f (x) + (ρ/2) k Ax + Bzt − c + µt k22 ), x

zt+1 := arg min(g(z)+(ρ/2) k Axt+1 +Bz−c+µt k22 ) and z

µt+1 := µt +Axt+1 +Bzt+1 −c. Actually, these two forms of ADMM are clearly equivalent, but the scaled form of ADMM is often more convenient than the unscaled form [37]. Hence, the scaled form will be used.

2) ADMM-Based Spectrum Band Sharing: To determine the optimal spectrum band allocation policy, we need to solve

s.t.

KX 1 +K2

i6=j

aij = 1, ∀j ∈ [1, K]

i=1

The constraint means that each band can only be allocated to a one-hop user or a group of two-hop users. In fact, problem (9) is a linear programming problem and hence it is quite suitable to solve it using ADMM algorithm [37]. To apply ADMM to the spectrum allocation problem (9), let x ∈ R(K1 +K2 )K×1 be the variable vector, which consists of one of the permutation of variables {aij , ∀i, j}, and z ∈ R(K1 +K2 )K×1 be an auxiliary vector, which consists of the same permutation of {zij , ∀i, j}. Also, we define as the set of variable vectors, which satisfy PK1Φ+K 2 constraints aij = 1, ∀j. Inspired by [34], to deal i=1 with the constraints, we introduce an indicator function g(z) such that g(z) = 0 when z ∈ Φ; otherwise, g(z) = +∞. With these notations above, problem (9) of maximizing UBSs on set Φ is equivalent to arg min{−UBSs (x) + g(z)} x,z

(10)

s.t. x − z = 0 which is essentially a general form consensus problem with regularization [37], because the objective function −UBSs (x) + g(z) and the constraint x − z = 0 are separable across each spectrum band j. Hence, the auxiliary variable z can be viewed as the global consensus variable, the constraint x − z = 0 is the consensus constraint, and the indicator function g(z) can be regarded as the regularization function. As mentioned above, the scaled form ADMM will be adopted. Hence, the augmented Lagrangian in scaled form can be given as Lρ (x, z, µ) = −UBSs (x) + g(z) − (ρ/2) k µ k22 +(ρ/2) k x − z + µ k22 , where µ is the scaled dual variable vector, and it consists of scaled dual variables µij corresponding to aij . Based on the iterations of scaled form ADMM, the iterations of ADMM for the considered problem can be written as equation (11) to (13) on the top of next page, where t stands for the iteration index of the ADMM algorithm. The basic idea behinds the ADMM iterations is that we first minimize the unconstraint augmented Lagrangian with respect to variables aij in x−update, and then project xt+1 + µt onto the feasible set Φ of the considered problem (9). Based on the analysis above, the ADMM-based spectrum band sharing algorithm is summarized as Algorithm 2. As we mentioned earlier, one of the important properties of the proposed ADMM-based algorithm is its quick con-



xt+1

 

  ρ := arg min −UBSs (x) + (aij − [zij ]t + [µij ]t )2 x   2 i=1 j=1   K 1 +K2 X KX  ([aij ]t+1 + [µij ]t − zij )2 zt+1 := arg min z∈Φ   KX K 1 +K2 X

i=1

(12)

j=1

µt+1 := µt + xt+1 − zt+1

Algorithm 2 ADMM-based spectrum band sharing algorithm 1: Initialize the number of one-hop users K1 , the number of groups of two-hop users K2 , the number of spectrum bands K, the initial spectrum band demand bj , the spectrum band allocation indicators x0 = 0, z0 = 0, µ0 = 1, iteration time t=0 and the stop threshold ε; 2: for k xt+1 − xt k2 > ε do 3: Update xt+1 via Eq. (11); 4: Update zt+1 via equation (12); 5: Update µt+1 via equation (13); 6: t = t + 1; 7: end for 8: Output spectrum band allocation indicators x and compute the optimal spectrum demand bj via equation (8).

(11)

2

2

(13)

2

∂ UT 2 that ∂∂cU2T ∂∂cU2T − ( ∂c ) > 0 when ν satisfies one of i ∂cj i j the conditions in Property 1. Hence, the concavity of (14) is proved. In practical multi-user and multi-carrier systems, the number of bands K is always large enough (e.g., K ≥ 10). Therefore, according to Property 1, the utility function is usually concave for most ν. Hence, the optimal price c∗j can be obtained by T solving ∂U ∂cj = 0. Then, we have PK PK 2ν i=1 cj − ν i=1 wj − νKκ −2cj + κ + wj + =0 1−ν (1 − ν)[1 + ν(K − 1)]

vergence to a modest accuracy of the optimal solution4 . The convergence of Algorithm 2 is guaranteed by the linearity of problem (9) [37].

After several manipulations, we get a closed-form solution κ + wj c∗j = (15) 2 where κ is same as that in (8). We can realize that the optimal price is jointly determined by the power allocation policy in Stage III, the band allocation policy in Stage II and the cost of each band at the spectrum providers.

C. Stage I: Bandwidth Pricing

D. Interplays and the Stackelberg Equilibrium

In stage I, to maximize their total profit, the spectrum providers need to determine the optimal price according to the band demand of BS-VRM. After substituting the optimal band demand (8) into the utility function in (6), we have # " PK K X ν(Kκ − i=1 ci ) κ − cj − (cj − wj ) UT = 1−ν (1 − ν)[1 + ν(K − 1)] j=1 (14) In order to obtain the optimal price vector c, we investigate the property of the utility function UT . Then, we have Property 1: The utility function in (14) is jointly concave with respect to the price vector c, when the band substitutability parameter ν satisfies one of the following conditions: S 1 2 ) ( 1−K , 1), when K 6= 1, 3; 1) ν ∈ (−1, 3−K 2) ν ∈ (−1, 1), when K = 1; 3) ν ∈ (− 21 , 1), when K = 3. Proof: By calculating the second-order derivatives of UT 2 4ν−2Kν−2 with respect to the price, we have ∂∂cU2T = (1−ν)[1+ν(K−1)]

Up to now, each stage of the three-stage Stackelberg game has been solved. However, it is easy to realize that: 1) the energy-efficient power allocation policy in stage III depends on the band allocation policy in stage II, 2) the optimal band demand and band allocation policy in stage II are closely related to the power allocation policy in stage III and the optimal price in stage I, 3) the optimal price for each band in stage I are jointly determined by the power allocation policy in stage III and the band allocation policy in stage II. Hence, to get the Stackelberg equilibrium [36], we must take these interplays into account. Firstly, we investigate the existence and uniqueness of the Stackelberg equilibrium. Proposition 1: The optimal energy-efficient power allocation policy in Subsection IV-A, the optimal band demand b∗j in (8) and the optimal band price c∗j in (15) are the subgame perfect equilibrium in each stage, respectively. Proof: The three-stage Stackelberg game can be regarded as an extensive game, and then each stage is a subgame. In stage I, the optimal price in (15) can maximize the total profit of the spectrum providers because of the concavity of its utility function in (14). That is to say there is no other better choice for the spectrum providers. Therefore, the optimal price is the subgame perfect equilibrium for stage I. Similarly, due to the

and

∂ 2 UT ∂ci ∂cj

i

=

2ν (1−ν)[1+ν(K−1)] .

Then, it is easy to verify

4 It is worth noting that, when the accuracy is compromised to get fast convergence in stage II, the utility of BS providers and spectrum providers might be slightly reduced.



Based on Proposition 1, we know that every subgame perfect equilibrium is a Nash equilibrium [36]. Therefore, there exists a Stackelberg equilibrium for the three-stage Stackelberg game. Because each subgame perfect equilibrium solved above is unique, the three-stage Stackelberg equilibrium is also unique. Hence, the existence and uniqueness of the Stackelberg equilibrium are guaranteed. Based on the analysis above, we can develop the following iterative algorithm to obtain the Stackelberg equilibrium solution. Algorithm 3 Energy-aware virtual resource management algorithm based on Stackelberg game 1: Give a default band price cj for the spectrum providers; do 2: Perform the optimal power allocation using Algorithm 1 at BS-VRM and RS-VRM; Allocate the bands to different users using Algorithm 2; Decide the optimal band demand based on (8) at BS-VRM; [n+1] using (15); 3: Update the price cj [n+1]

while{ 4:

kcj

[n] −cj k1 [n] kcj k1

> ǫ}

Output the energy-aware power allocation strategy and spectrum band sharing scheme.

E. Analysis of Convergence and Feasibility In Algorithm 3, the BS-VRM needs to decide the optimal band demand and assign the bands to different users in each iteration. Also, the BS-VRM and RS-VRM will perform the optimal power allocation. The algorithm will stop when the prices converge. Therefore, Algorithm 3 will converge to the Stackelberg equilibrium. This is because the optimal band price is a best reaction function of the optimal power allocation policy and the band allocation policy. Hence, when the prices converge, the power allocation policy and the band allocation policy will also achieve their optimum. Therefore, according to Proposition 1, the convergence of Algorithm 3 is guaranteed. This will also be verified in the simulation results. Moreover, since the resource allocation in the whole network is realized in a distributed manner, the BS-VRM, RSVRM and spectrum providers only need to optimize their utility based on the response of other entities. Comparing to the centralized schemes which optimizes a unified objective in a centralized manner, the computational complexity and the signaling overheads of the proposed game-based approach can be reduced significantly. V. S IMULATION R ESULTS AND D ISCUSSIONS In this part, we will first compare the performance of our proposed virtualized FDR scheme with different existing

7000 The total utility of base station providers UBSs

quasi-concavity of function (4) and the concavity of function (5), the optimal power allocation strategy and the optimal band demand are also the subgame perfect equilibrium for stage III and stage II, respectively. Therefore, Proposition 1 is proved.

6000

5000

4000

3000

2000 Our proposed scheme with FDR and virtualization Existing scheme with FDR but without virtualization Existing scheme without FDR and virtualization

1000

0 10

20

30

40 50 The number of user

60

70

Fig. 3. The total utility of BS providers for different schemes with different numbers of users. There are three BS providers, one RS provider and two SPs. The number of cells is one and the variance of residual loop interference δe2 = 10−4 .

schemes. Then, we compare the proposed game-based resource management algorithm with two classical algorithms in terms of energy efficiency and spectrum efficiency. At last, the convergence of the proposed game will be also demonstrated. The simulation setups are given as follows. The radii of each cell and the coverage of the shared relay are 1km and 0.33km, respectively. The 3GPP path loss model is used to realize different channels [7]. The small scale fading from the RS to two-hop users and that from the BS to one-hop users are modeled as independent and identically distributed Rayleigh random variables. Since a strong line of sight is generally existed between the BS and the RS in practice, the channel from BS to RS is modeled as Rician random variables with Rician factor κ = 6dB. The total bandwidth of each spectrum provider is 20MHz and the whole bandwidth can be divided into multiple subbands according to the demand of BS providers. There are three BS providers, one RS provider and two SPs. The SPs have two kinds of subscribers: one-hop users and two-hop users. The two-hop users are divided into multiple groups. The RS has three antennas. The number of cells and users will be variable in different simulations. The circuit power is pb = pr = 100mW , the noise variance is set to δ 2 = −128dBm [7] and the band substitutability parameter is ν = 0.2 in all the results. A. The Comparison of Different Schemes in Terms of Utility In this subsection, we compare the following schemes: (I) Existing scheme without FDR and virtualization (only half-duplex relaying is adopted) [23]; (II) Existing scheme with FDR but without virtualization [19]; (III) Our proposed scheme with FDR and virtualization. As shown in Fig. 3, we evaluate the total utility of BS providers for different schemes with different numbers of users in a single cell environment.



950 Our proposed scheme with FDR and virtualization Existing scheme with FDR but without virtualization Existing scheme without FDR and virtualization

The total utility of relay station provider

900

850

800

750

700

650

600 −4 10

Also, Fig. 4 illustrates the average transmission rate of users for different schemes when the total number of user is 60 in two SPs. As can be seen from Fig. 3 and Fig. 4, the proposed virtualized FDR network performs better than the existing scheme without FDR and virtualization as well as the existing scheme with FDR but without virtualization. The reasons are given as follows. On one hand, when FDR is used, the relay can transmit and receive simultaneously on the same band. Hence, less spectrum resources are needed to achieve the same transmission rate. Therefore, less cost is involved in spectrum resource and higher utility can be obtained for the base station providers. On the other hand, when virtualization is used, the relay and the users can access to the base stations with better channel conditions. In this way, less power consumption is needed and hence higher energy efficiency can be achieved. Therefore, more revenue can be obtained for the base station providers. Meanwhile, the users can also get a better service quality. In addition to the above observations, we also evaluate the impacts of the residual loop interference and the network scale, as shown in Fig. 5 and Fig. 6. It can be found that, when the loop interference is suppressed sufficiently (i.e., the residual loop interference is low enough), the proposed scheme with FDR performs better than the existing scheme without FDR. However, when the residual loop interference becomes large enough, the existing scheme without FDR performs better than our proposed scheme. This is because larger residual loop interference will deteriorate the performance of FDR. That is to say, the effective loop interference cancellation technologies [8] are important for the performance of FDR networks. It also can be observed in Fig. 6, when we extend the network scale by increasing the number of cells, the

−2

10

−1

0

10

10

Fig. 5. The total utility of relay station provider for different schemes with different level of residual loop interference. There are three BS providers, one RS provider and two SPs. The number of cells is one and the total number of user is 60 in two SPs. The total utility of base station providers and relay station provider

Fig. 4. The average transmission rate of users for different schemes when the total number of user is 60 in two SPs and the variance of residual loop interference δe2 = 10−4 . (I) Existing scheme without FDR and virtualization; (II) Existing scheme with FDR but without virtualization; (III) Our proposed scheme with FDR and virtualization.

−3

10

The variance of residual loop interference δ2e

4

4

x 10

3.5 3 2.5 2 1.5 1 Our proposed scheme with FDR and virtualization Existing scheme with FDR but without virtualization Existing scheme without FDR and virtualization

0.5 0

0

1

2

3 4 The number of cells

5

6

7

Fig. 6. The total utility of base station providers and relay station provider for different schemes with different numbers of cells. The variance of residual loop interference δe2 = 10−4 .

total utility of base station providers and relay station provider increases almost linearly with the number of cells. In other words, our proposed scheme is also applicable to large scale networks. B. The Comparison of Different Algorithms in Terms of Energy Efficiency and Spectrum Efficiency In this subsection, we evaluate the performance of the game-based virtual resource management algorithm in terms of energy efficiency and spectrum efficiency, as shown in Fig. 7 and Fig. 8. We compare the performance of the pro-


This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2015.2497360, IEEE Transactions on Vehicular Technology

The average energy efficiency for the whole network (kbits/Joule)

11

WFPA and APA schemes first increases and then decreases. The above observations reveal that there exists a tradeoff between energy efficiency and spectrum efficiency, as in other wireless networks [18].

90 The proposed game WFPA with Ptotal=20dBm

80

APA with Ptotal=20dBm

70

WFPA with Ptotal=25dBm APA with Ptotal=25dBm

60 50

WFPA with Ptotal=30dBm

C. The Convergence of the Proposed Game


At last, the convergence of the proposed game is verified in Fig. 9 and Fig. 10. For ease of illustration, we only consider a simple scenario with three one-hop users and one group of two-hop users. Each one-hop user or the group of two-hop users can only be allocated one spectrum band. As shown in Fig. 9(a), in the first stage of the proposed game approach, there is only one best spectrum price for each spectrum provider. Similarly, as shown in Fig. 9(b) and Fig. 9(c), there is also only one optimal action in stage two/three for the base station providers/relay station provider. That’s to say, the action taken in each stage is the best reaction for each stage. Therefore, there exists an unique subgame perfect equilibrium for each stage. This guarantees the existence and uniqueness of the three-stage Stackelberg equilibrium of the proposed game. Also, Fig. 10 illustrates the global convergence of the proposed three-stage game. We can observe that the prices for spectrum providers and the spectrum band demand for the base station providers converge soon at the same time. In addition, we can also see that higher spectrum demand will lead to higher price, which coincides with the linear structure assumption of the price and demand. These results jointly demonstrate the effectiveness and convergence of the proposed three-stage Stackelberg game.

40 30 20 10 0

0

5 10 15 The average signal to noise ratio for users (dB)

20

Fig. 7. The comparison of energy efficiency for different resource management algorithms. The number of cell is one, the variance of residual loop interference δe2 = 10−4 and Ptotal is the total power constraint for WFPA and APA scheme.

The average transmission rate for users (Mbits/s)

1.4 The proposed game WFPA with Ptotal=20dBm

1.2


1


0.8


APA with Ptotal=25dBm APA with Ptotal=30dBm

0.6

0.4

VI. C ONCLUSIONS

0.2

0

0

5 10 15 The average signal to noise ratio for users (dB)

20

Fig. 8. The comparison of transmission rate for different resource management algorithms. The number of cell is one, the variance of residual loop interference δe2 = 10−4 and Ptotal is the total power constraint for WFPA and APA scheme.

posed game with two classical algorithms: water-filling power allocation algorithm (WFPA) and average power allocation algorithm (APA). Both WFPA and APA scheme adopt the spectrum allocation algorithm in [7] to maximize the total transmission rate. From Fig. 7, we can observe that the proposed game outperforms WFPA scheme and APA scheme in terms of energy efficiency. This is because we have taken the energy efficiency into account in the optimized utility functions in this paper. However, as shown in Fig. 8, the higher performance in energy efficiency of the proposed game is obtained at the expense of lower average transmission rate. In addition, by increasing the total transmission power from 20dBm to 30dBm, the average transmission rate of WFPA and APA scheme increases, however, the energy efficiency of

AND

F UTURE W ORK

In this paper, we introduced the idea of wireless virtualization into full-duplex relaying cellular networks. We considered four logical roles in cellular networks with FDR and virtualization: spectrum provider, base station provider, relay station provider and service provider. Moreover, we investigated the problem of energy-aware joint bandwidth sharing and power allocation in virtualized cellular network with shared FDR. The problem of energy-aware virtual resource management was formulated as a three-stage Stackelberg game. In stage I, the spectrum providers offer the price of each band to the BS providers. In stage II, the BS providers purchase bands from spectrum providers and allocate the bands to different users. In stage III, the RS provider performs the energy-efficient power allocation for two-hop users. Then, we analyzed the subgame perfect equilibrium for each stage using backward induction method and developed an iterative algorithm to obtain the Stackelberg equilibrium. In addition, the existence and uniqueness of the Stackelberg equilibrium were proved through theoretical analysis and verified by computer simulations. Simulation results demonstrated that the proposed virtualized FDR network can benefit from both FDR and virtualization technologies at the same time. Also, the proposed three-stage virtual resource management game is effective. In our future



The spectrum price for the first spectrum provider c

1

25

330

320 Subgame perfect equilibrium for stage one 310

300 The spectrum price for the first spectrum provider c

1

The spectrum price for the second spectrum provider c

2

290

The spectrum price for the third spectrum provider c

3

The spectrum price for the fourth spectrum provider c 280

8

9

10 11 12 13 14 The spectrum price for each spectrum provider

4

15

16

(a) The subgame of stage one.

Price or band demand corresponding to each spectrum provider

The total utility of spectrum providers UT

340

2

Spectrum demand from the second spectrum provider b

The total utility of base station providers UBSs

2

The spectrum price for the third spectrum provider c

20

3

Spectrum demand from the third spectrum provider b

3

The spectrum price for the fourth spectrum provider c

4

Spectrum demand from the fourth spectrum provider b 15

4

10

5

0

2

4

6 8 Iteration times

10

12

14

230

220

Fig. 10. The convergence of the three-stage Stackelberg game. There are three one-hop users and one group of two-hop users. The number of cell is one and the variance of residual loop interference δe2 = 10−4 .

Subgame perfect equilibrium for stage two

210

200 Spectrum demand from the first spectrum provider b1

190

Spectrum demand from the second spectrum provider b2 Spectrum demand from the fourth spectrum provider b4 0

5

10 Spectrum demand

15

R EFERENCES 20

(b) The subgame of stage two. 15.5

15

14.5 Subgame perfect equilibrium for stage three 14

13.5 The power for the first subchannel q1

13

The power for the second subchannel q2 The power for the third subchannel q3

12.5

work, we will consider the tradeoff between energy efficiency and spectrum efficiency. In addition, the QoS guarantee and fairness for different users will also be investigated.

Spectrum demand from the third spectrum provider b3

180

170

Energy efficiency of the access link (kbits/Joule)

1

The spectrum price for the second spectrum provider c

0 240

Spectrum demand from the first spectrum provider b

0

0.2 0.4 0.6 0.8 Allocated power on each subchannel (W)

1

(c) The subgame of stage three. Fig. 9. The illustration of subgame perfect equilibrium. There are three one-hop users and one group of two-hop users. The number of cells is one and the variance of residual loop interference δe2 = 10−4 .

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Gang Liu (M’15) is currently a lecturer at the School of Information Science and Technology, Southwest Jiaotong University (SWJTU), Chengdu, China. He received the Ph.D. degree in Communication and Information Systems from Beijing University of Posts and Telecommunications (BUPT) in 2015, and the B.S. degree in Electronics and Information Engineering from Sichuan University (SCU) in 2010. He was also with the University of British Columbia and Carleton University as a visiting PhD student from Nov. 2013 to Nov. 2014. His current research interests include 5G cellular networks, full-duplex wireless, network virtualization, resource management, cross-layer design, and TCP/IP protocol optimization in satellite communication systems. Dr. Liu has authored or co-authored more than 15 technical papers in international journals and conference proceedings. He won the Excellent Doctoral Dissertation Award of BUPT in 2015, the Best Paper Award in IEEE ICC’2014, and the Second Prize in the National Undergraduate Electronic Design Contest of China in 2009. He has also served as reviewers for numerous journals and conferences, such as IEEE Transactions on Vehicular Technology, Digital Signal Processing, Wireless Networks, International Journal of Communication Systems, China Communications, KSII Transactions on Internet and Information Systems, IEEE ICC’2012, IEEE Globecom’2013, IEEE WCNC’2014, CloudCom’2015, 5GiSC 2015 and so on.



F. Richard Yu (S’00-M’04-SM’08) received the PhD degree in electrical engineering from the University of British Columbia (UBC) in 2003. From 2002 to 2004, he was with Ericsson (in Lund, Sweden), where he worked on the research and development of wireless mobile systems. From 2005 to 2006, he was with a start-up in California, USA, where he worked on the research and development in the areas of advanced wireless communication technologies and new standards. He joined Carleton School of Information Technology and the Department of Systems and Computer Engineering at Carleton University in 2007, where he is currently an Associate Professor. He received the IEEE Outstanding Leadership Award in 2013, Carleton Research Achievement Award in 2012, the Ontario Early Researcher Award (formerly Premier’s Research Excellence Award) in 2011, the Excellent Contribution Award at IEEE/IFIP TrustCom 2010, the Leadership Opportunity Fund Award from Canada Foundation of Innovation in 2009 and the Best Paper Awards at IEEE ICC 2014, Globecom 2012, IEEE/IFIP TrustCom 2009 and Int’l Conference on Networking 2005. His research interests include cross-layer/cross-system design, security, green IT and QoS provisioning in wireless-based systems. He serves on the editorial boards of several journals, including Co-Editorin-Chief for Ad Hoc & Sensor Wireless Networks, Lead Series Editor for IEEE Transactions on Vehicular Technology, IEEE Communications Surveys & Tutorials, EURASIP Journal on Wireless Communications Networking, Wiley Journal on Security and Communication Networks, and International Journal of Wireless Communications and Networking, a Guest Editor for IEEE Transactions on Emerging Topics in Computing special issue on Advances in Mobile Cloud Computing, and a Guest Editor for IEEE Systems Journal for the special issue on Smart Grid Communications Systems. He has served on the Technical Program Committee (TPC) of numerous conferences, as the TPC Co-Chair of IEEE GreenCom’15, INFOCOM-MCV’15, Globecom’14, WiVEC’14, INFOCOM-MCC’14, Globecom’13, GreenCom’13, CCNC’13, INFOCOM-CCSES’12, ICC-GCN’12, VTC’12S, Globecom’11, INFOCOM-GCN’11, INFOCOM-CWCN’10, IEEE IWCMC’09, VTC’08F and WiN-ITS’07, as the Publication Chair of ICST QShine’10, and the CoChair of ICUMT-CWCN’09. Dr. Yu is a registered Professional Engineer in the province of Ontario, Canada.

Victor C.M. Leung (S’75-M’89-SM’97-F’03) received the B.A.Sc. (Hons.) degree in electrical engineering from the University of British Columbia (U.B.C.) in 1977, and was awarded the APEBC Gold Medal as the head of the graduating class in the Faculty of Applied Science. He attended graduate school at U.B.C. on a Natural Sciences and Engineering Research Council Postgraduate Scholarship and completed the Ph.D. degree in electrical engineering in 1981. From 1981 to 1987, Dr. Leung was a Senior Member of Technical Staffin the satellite systems group at MPR Teltech Ltd. He started his academic career in the Department of Electronics at the Chinese University of Hong Kong in 1988. He returned to U.B.C. as a faculty member in 1989, where he currently holds the positions of Professor and TELUS Mobility Research Chair in Advanced Telecommunications Engineering in the Department of Electrical and Computer Engineering. He is a member of the Institute for Computing, Information and Cognitive Systems at U.B.C. He also holds adjunct/guest faculty appointments at Jilin University, Beijing Jiaotong University, South China University of Technology, the Hong Kong Polytechnic University and Beijing University of Posts and Telecommunications in China. Dr. Leung has co-authored more than 500 technical papers in international journals and conference proceedings, and several of these papers had been selected for best paper awards. His research interests cover broad areas of wireless networks and mobile systems. Dr. Leung is a registered professional engineer in the Province of British Columbia, Canada. He is a Fellow of IEEE, the Engineering Institute of Canada, and the Canadian Academy of Engineering. He is a Distinguished Lecturer of the IEEE Communications Society. He is serving on the editorial boards of the IEEE Transactions on Computers, IEEE Wireless Communications Letters, Computer Communications, the Journal of Communications and Networks, and several other journals. He has served on the editorial boards of the IEEE Journal on Selected Areas in Communications - Wireless Communications Series, the IEEE Transactions on Wireless Communications and the IEEE Transactions on Vehicular Technology, and has guest-edited several journal special issues. He has served on the technical program committees of numerous international conferences. He is a General Cochair of GCN Workshop at ICC 2012, GCSG Workshop at Infocom 2012,FutureTech 2012, and CSA 2011. He co-chairs the TPC of the MAC and Cross-layer Design track of IEEE WCNC 2012. He chaired the TPC of the wireless networking and cognitive radio track in IEEE VTC-fall 2008. He was the General Chair of Chinacom 2011, MobiWorld and GCN Workshops at Infocom 2011, AdhocNets 2010, WC 2010, QShine 2007, and Symposium Chair for Next Generation Mobile Networks in IWCMC 2006-2008. He was a General Co-chair of BodyNets 2010, CWCN Workshop at Infocom 2010, ASIT Workshop at IEEE Globecom 2010, MobiWorld Workshop at IEEE CCNC 2010, IEEE EUC 2009 and ACM MSWiM 2006, and a TPC Vicechair of IEEE WCNC 2005.

Hong Ji received the B.S. degree in communications engineering and the M.S. and Ph. D degrees in information and communications engineering from the Beijing university of Posts and Telecommunications (BUPT), Beijing, China, in 1989, 1992, and 2002, respectively. From June to December 2006, she was a Visiting Scholar with the University of British Columbia, Vancouver, BC, Canada. She is currently a Professor with BUPT. She also works on national science research projects, including the HiTech Research and Development Program of China (863 program), The National Natural Science Foundation of China, etc. Her research interests include heterogeneous networks, peer-to-peer protocols, and cognitive radio.
